Digital ACT Math Practice Question #1281
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Check boundaries: $x = 3 \implies \sqrt{0}/(-4) = 0$ (valid, eliminates strict inequality). $x = 7 \implies$ division by zero (must be excluded). Instantly identifies $x \ge 3$ and $x \ne 7$.
For $f(x)$ to be real-valued, two conditions must hold simultaneously: 1. The radicand under the square root must be nonnegative: $4x - 12 \ge 0 \implies 4x \ge 12 \implies x \ge 3$. 2. The denominator cannot be zero: $x - 7 \ne 0 \implies ...
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
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